q.append(first_node)
visited.add(first_node)
while q:
node = q.popleft()
print(node, end=" ")
for elem, connection in enumerate(g[node]):
if elem not in visited and connection and connection < math.inf:
q.append(elem)
visited.add(elem)
if __name__ == "__main__":
g = GraphM(4)
g.add_edge(0, 1)
g.add_edge(0, 2)
g.add_edge(1, 2)
g.add_edge(2, 0)
g.add_edge(2, 3)
g.add_edge(3, 3)
print("bfs starting at node 2")
breadth_first_travel(g.graph, 2)
print()
print("bfs starting at node 1")
breadth_first_travel(g.graph, 1)
print()
print("bfs starting at node 0")
breadth_first_travel(g.graph, 0)
print()
print("bfs starting at node 3")
path.pop(-1)
return total
path: list = [source]
for source, distance in enumerate(graph[source]):
if 0 < distance < math.inf and backtrack(source, distance, {source},
0) > k:
return path
return []
if __name__ == "__main__":
g = GraphM(9)
g.add_edge(0, 1, 4)
g.add_edge(0, 7, 8)
g.add_edge(1, 2, 8)
g.add_edge(1, 7, 11)
g.add_edge(2, 3, 7)
g.add_edge(2, 5, 4)
g.add_edge(2, 8, 2)
g.add_edge(3, 4, 9)
g.add_edge(3, 5, 14)
g.add_edge(4, 5, 10)
g.add_edge(5, 6, 2)
g.add_edge(6, 7, 1)
g.add_edge(6, 8, 6)
g.add_edge(7, 8, 7)
print(path_greater(g.graph, 0, 60, g.num_vertices))
"""
visited = set()
graph_list = graph.graph
mother = None
for vertex in range(graph.num_vertices):
if vertex not in visited:
visited = dfs(graph_list, vertex, visited)
mother = vertex
visited = set()
dfs(graph_list, mother, visited) # check if all others can reach from here
if any(vertex not in visited for vertex in range(graph.num_vertices)):
return None
return mother
if __name__ == "__main__":
g = GraphM(7, "directed")
g.add_edge(0, 2)
g.add_edge(1, 3)
g.add_edge(0, 1)
g.add_edge(4, 1)
g.add_edge(6, 4)
g.add_edge(5, 6)
g.add_edge(5, 2)
g.add_edge(6, 0)
print("A mother vertex is", get_mother_vertex(g))
All nodes with less in-degree can safely add an edge
to all nodes with degrees less than them.
For nodes with same in-degree, we can safely add a directed node in one direction.
Solution from Kahn's algorithm can be used here
time complexity: O(V+E)
"""
sorted_vertices = topological_sort_kahn_algorithm(graph, vertices)
res: list = []
visited: set = set()
for src in sorted_vertices:
for dest, connected in enumerate(graph[src]):
if connected not in (0, 1) and dest not in visited:
res.append((src, dest))
graph[src][dest] = 1
visited.add(src)
return res, len(res)
if __name__ == "__main__":
g = GraphM(6, "directed")
g.add_edge(4, 0)
g.add_edge(4, 1)
g.add_edge(5, 2)
g.add_edge(5, 0)
g.add_edge(2, 3)
g.add_edge(3, 1)
print(*add_edges_safely(g.graph, g.num_vertices))
def is_cyclic(graph: list, vertices: int) -> bool:
subsets: list = [Subset(v, 0) for v in range(vertices)]
for u in range(vertices):
pu = find(u, subsets)
for v, connection in enumerate(graph[u]):
if u != v and connection == 1:
pv = find(v, subsets)
if pu == pv:
return True
union(pu, pv, subsets)
return False
if __name__ == "__main__":
g = GraphM(3)
g.add_edge(0, 1)
g.add_edge(1, 2)
g.add_edge(0, 2)
if is_cyclic(g.graph, g.num_vertices):
print("Graph contains cycle")
else:
print("Graph does not contain cycle")
ts_list.append(element)
visited.add(element)
for vertex, connected in enumerate(graph[element]):
if connected == 1:
indegree_list[vertex] -= 1
if indegree_list[vertex] == 0:
queue.append(vertex)
return ts_list if len(visited) == len(graph) else []
if __name__ == "__main__":
g = GraphM(7, "directed")
g.add_edge(0, 2)
g.add_edge(1, 2)
g.add_edge(1, 3)
g.add_edge(2, 4)
g.add_edge(3, 5)
g.add_edge(4, 5)
g.add_edge(5, 6)
print(topological_sort_using_dfs(g.graph, g.num_vertices))
print(topological_sort_kahn_algorithm(g.graph, g.num_vertices))
g = GraphM(6, "directed")
g.add_edge(5, 0)
g.add_edge(5, 2)
g.add_edge(2, 3)
g.add_edge(3, 1)
gray_stack.append(neighbor)
gray_set.add(neighbor)
initial_set.remove(neighbor)
if not found: # if sub-graph is completely explored, move the node to processed
gray_set.remove(cur_node)
processed_set.add(cur_node)
else:
cur_node = initial_set.pop()
gray_set.add(cur_node)
gray_stack.append(cur_node)
if __name__ == "__main__":
g = GraphM(4, "directed")
g.add_edge(0, 1)
g.add_edge(0, 2)
g.add_edge(1, 2)
g.add_edge(2, 0)
g.add_edge(2, 3)
g.add_edge(3, 3)
print("First Graph")
for i in range(g.num_vertices):
print(g.graph[i])
detect_print_cycle(g.graph, g.num_vertices)
detect_cycle_dfs(g.graph, g.num_vertices)
g = GraphM(6, "directed")
g.add_edge(0, 1)